On the Density of Positive Proper Efficient Points in a Normed Space

K. F. Ng and X. Y. Zheng
Additional contact information
K. F. Ng: Chinese University of Hong Kong, Shatin
X. Y. Zheng: Chinese University of Hong Kong, Shatin

Journal of Optimization Theory and Applications, 2003, vol. 119, issue 1, No 7, 105-122

Abstract: Abstract In the context of vector optimization and generalizing cones with bounded bases, we introduce and study quasi-Bishop-Phelps cones in a normed space X. A dual concept is also presented for the dual space X*. Given a convex subset A of a normed space X partially ordered by a closed convex cone S with a base, we show that, if A is weakly compact, then positive proper efficient points are sequentially weak dense in the set E(A, S) of efficient points of A; in particular, the connotation weak dense in the above can be replaced by the connotation norm dense if S is a quasi-Bishop-Phelps cone. Dually, for a convex subset of X* partially ordered by the dual cone S +, we establish some density results of positive weak* efficient elements of A in E(A, S +).

Keywords: Vector optimization; efficient points; positive proper efficient points; quasi-Bishop-Phelps cones; normed spaces (search for similar items in EconPapers)
Date: 2003
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1023/B:JOTA.0000005043.39887.76 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:119:y:2003:i:1:d:10.1023_b:jota.0000005043.39887.76

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1023/B:JOTA.0000005043.39887.76

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().